This paper introduces analytical solutions to gap waveguide slot antenna structures. The reciprocity method is used for the analysis by exploiting Green's function of a bed of nails structure employing a homogenized plane-wave spectral-domain approach. Green's function is found using parallel plate waveguide and surface admittance concepts. The spectral surface admittance of the pin structure is calculated using asymptotic boundary condition (ABC), and the unknown antenna slot currents are solved using moment methods. The structure is designed to have a cutoff frequency of 10-15 GHz, and the central operating frequency of the slot is 12.5 GHz. This approach is applied to the specific geometry of a propagating ridge gap waveguide single transverse broad wall slot antenna structure. The equivalent series impedance and far zone fields and patterns are calculated, and the results are compared with a full-wave commercial software, and they are proved to be accurate.INDEX TERMS Artificial magnetic conductor, asymptotic boundary condition, gap waveguide slot antenna, ridge gap waveguide, spectral domain approach.